C语言 黄金分割法确定极小值

标签：const   amp   ati   while   void   指针   ret   else   turn   

#include <stdio.h>
#include <math.h>

#define F(x)	(3*x*x*x-4*x+2)	


double fun1(double x);
void goAndBackSectionPrint(double x1, double h, double (*f)(double), double *ret1, double *ret2);
void goldenSecton(double x0, double h, double (*f)(double), double e);

int main(void){
	goldenSecton(0, 1, fun1, 0.1);
	return 0;
}

//进退法打印区间
//x1	搜索初值
//h	搜索步长
//f 	待搜索函数f(x)的指针
//ret1 ret2 返回区间指针
void goAndBackSectionPrint(double x1, double h, double (*f)(double), double *ret1, double *ret2){
	double a1 = x1;
	double y1 = (*f)(a1);	
	double a2 = a1 + h;
	double y2 = f(a2);	
	double a3 = 0;
	double y3 = 0;
	
	if(y2 > y1){
		h = -h;
		a3 = a1;
		y3 = y1;
		
		a1 = a2;
		y1 = y2;
		a2 = a3;
		y2 = y3;
	}

	a3 = a2 + h;
	y3 = f(a3);
	
	while(y3 < y2){
		h = 2*h;
		a1 = a2;
		y1 = y2;
		a2 = a3;
		y2 = y3;
		
		a3 = a2 + h;
		y3 = f(a3);
	}
	
	*ret1 = a1;
	*ret2 = a3;
	
	printf("a1 = %f, y1 = %f.\n", a1, y1);
	printf("a2 = %f, y2 = %f.\n", a2, y2);
	printf("a3 = %f, y3 = %f.\n", a3, y3);
}


//黄金分割法
	//进退法打印区间
	//x0	搜索初值
	//h	搜索步长
	//f 	待搜索函数f(x)的指针
//e 	误差要求
void goldenSecton(double x0, double h, double (*f)(double), double e){
	double a, b;
	const double ratio = 0.618;
	goAndBackSectionPrint(x0, h, f, &a, &b);
	printf("确定区间为 [%f, %f].\n", a, b);
	
	double a1 = b - ratio*(b - a);
	double y1 = f(a1);
	double a2 = a + ratio*(b - a);
	double y2 = f(a2);

	do{
		if(y1 >= y2){
			a = a1;
			a1 = a2;
			y1 = y2;
			
			a2 = a + ratio*(b - a);
			y2 = f(a2);
		}
		else{
			b = a2;
			a2 = a1;
			y2 = y1;
			
			a1 = b - ratio*(b - a);
			y1 = f(a1); 
		}
	}while((fabs((b-a)/b) >= e) || (fabs((y2-y1)/y2) >= e));
	
	printf("a = %f, f(a) = %f.\n", a, f(a));
	printf("b = %f, f(b) = %f.\n", b, f(b));
	double minVal = (a+b)/2;
	printf("函数的最小值点为：%f。\n", minVal);
	printf("函数的最小值为：  %f。\n", f(minVal));
	
}



double fun1(double x){
	return F(x);
}

C语言 黄金分割法确定极小值

标签：const   amp   ati   while   void   指针   ret   else   turn   

原文地址：https://www.cnblogs.com/ritchie0307/p/12964067.html